Lasker vs. Morphy: Psychology enters the battle !
Dr. Emanuel Lasker (1868-1941) dominated the chess world for approx. 30 years (he was the formal World champion from 1894 when he defeated Steinitz in New York until 1921 when he lost for Capablanca in Havana), a good 50 years after Morphy. In my opinion, they shared many of the same characteristics in terms of playing style.
However, with Lasker (as with Steinitz, not Morphy) we have facts - he left behind articles and books to document his style attributes. Lasker was a mathematician; one of his more interesting thesis for chess novices (he wrote a teaching book in 1927) was to demand proof (!) for pieces of advice on positions or combinations. His view was that most positional judgments were objectively false, and that the key was to trust your own judgment (of course, this was long before the age of the computer).
Speaking of proof - I had an interesting exchange a few weeks back regarding the statistics being presented in the "Explore Games and Openings" section of chess.com, arguing that these statistics, although indicating main lines, certainly cannot be interpreted as cause-effect relationships (... black did not win because of these moves. He won for different reasons, but once having won - his opening moves were such and such. This is correlation of course, not cause-effect). To use these opening moves as verifications for "we should now do" pieces of advice, is questionable to say the least. I believe Lasker would have agreed ...
... and so back to Dr. Lasker: He was a "battleground" and positional player, just as Morphy. However, with Lasker the arsenal of psychological weapons were added to the battleground. Lasker studied his opponents, consciously selecting openings and playing style elements that were to a maximum degree uncomfortable for his counterparts. In this way he "moved" the game to settings which represented a stronger likelihood that his counterpart would make a mistake. He did not himself necessarily choose the "best move", he chose the move that represented a strong dislike for his enemy! There were also hypothesis that he consciously did "poor moves" and brought himself to the brink of disaster in order to sharpen his fighting spirit. His key attitude was that when you are at war, all weapons should be exploited.
Here is an end game study from the world championship in 1894- Lasker vs. Steinitz: